Recently, single-symbol Maximum-Likelihood (ML) decodable Distributed Space-Time Block Coding (DSTBC) has been developed for use in cooperative diversity networks. However, the symbol rate of the DSTBC decreases with the number of relays. This issue can be addressed if the Channel Phase Information (CPI) of the first-hop is exploited, and such code is referred to as DSTBC-CPI. Some complex single-symbol decodable DSTBCs-CPI were reported in the literature. However, no upper-bound on the symbol rate of such DSTBC-CPI has been derived, although it is a fundamental issue. Furthermore, finding a tight (more preferably achievable) upper-bound is essential to check if any developed code is optimum or not.